Mechanical remote centre of motion (RCM) mechanisms are often used to construct robotic minimally-invasive surgical manipulators, such that potential damage on the incision ports is eliminated. Current parallelogram-based RCM linkages (PB-linkage) typically have large footprints that compromise optimal surgical operations. A novel cable system with remote centre of motion is proposed to reduce the footprint. The RCM function of the cable system is proven mathematically. A new approach based on constraint analysis is conducted to determine the magnitudes of tension. The results are validated by finite element analysis, hence proves the use of constraint approach and the functioning of the cable system. Upon verification, the footprint of the cable linkage is compared to that of a PB-linkage in a simplified surgical scenario through three approaches. The quantitative analysis shows that the cable linkage has a smaller footprint in more than half of the design points in all approaches. A prototype is built for proofing the concept of the cable linkage.